Minimum tone separation constrained mfsk scheme for ultrasonic communications

ABSTRACT

A method of encoding a plurality of data signals is disclosed. The method includes selecting a set of M ultrasonic frequencies, wherein each of the M ultrasonic frequencies differs from an adjacent frequency by at least a first frequency spacing, and wherein M is a positive integer. An encoder receives the plurality of data signals. Each of the plurality of data signals is encoded by a respective set of Q of the M ultrasonic frequencies, wherein Q is a positive integer less than M. A minimum frequency separation between any pair of the Q ultrasonic frequencies of any respective set is greater than the first frequency spacing.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims the benefit under 35 U.S.C. 119(e) of U.S.Provisional Application No. 62/236,549 (TI-76451PS), filed Oct. 2, 2015,and of U.S. Provisional Application No. 62/236,579 (TI-76452PS), filedOct. 2, 2015, both of which are incorporated by reference herein intheir entirety.

BACKGROUND OF THE INVENTION

Embodiments of the present invention relate to encoding data signals forultrasonic communication through a multipath fading channel.

Ultrasound technology has been developed for practical applications suchmeasuring fluid velocity in a pipe, measuring characteristics of a pipeand of fluid in the pipe, ultrasonic communication through various mediasuch as metal pipes, underwater acoustic measurements, medicalapplications, and numerous other applications.

Referring to FIG. 1, for example, Hosman et al., “Design andCharacterization of an MFSK-Based Transmitter/Receiver for UltrasonicCommunication Through Metallic Structures,” IEEE Trans. OnInstrumentation and Measurement, Vol. 60, No. 12, pp. 3767-3774(December 2011) disclose an ultrasonic communication system forcommunicating through steel corner posts of shipping containers, whichis incorporated herein by reference in its entirety. The communicationsystem transmits multitone frequency-shift keyed (MFSK) data through thesteel corner posts by means of attached ultrasonic transducers to areceiver external to the shipping containers. The steel corner posts arecharacterized as a metal multipath fading channel. Hosman et al. employan MFSK encoding system as shown at FIG. 2. A data word is applied to asymbol encoder to selectively apply frequencies f₀ through f_(N-1) to asum circuit. The selected frequencies are then applied to an ultrasonictransducer for transmission through the steel corner posts. The MFSKsystem of Hosman et al. uses different combinations of Q summed tonesfrom N available tones to produce

$\begin{pmatrix}N \\Q\end{pmatrix}\quad$

MFSK symbols, where

$\begin{pmatrix}N \\Q\end{pmatrix}\quad$

is defined as N!/(Q!(N−Q)!). MFSK encoding advantageously producessubstantially more encoded symbols than traditional frequency shiftkeyed (FSK) encoding as shown at FIG. 3. Here, for example, N=32available tones will encode 5 bits (log₂ (32)) in each FSK symbol. Byway of comparison, MFSK will encode 29 bits or the integer portion oflog₂

$\begin{pmatrix}N \\Q\end{pmatrix}\quad$

for Q=16. This results in a significantly higher data rate for MFSKencoding with the same number of available tones. The present inventorshave realized a need to improve communication techniques through themultipath fading channel to further improve data throughput and reducesymbol error rate (SER). Accordingly, the preferred embodimentsdescribed below are directed toward improving upon the prior art.

BRIEF SUMMARY OF THE INVENTION

In a first embodiment of the present invention, a method of encoding aplurality of data signals is disclosed. The method includes selecting aset of M ultrasonic frequencies, wherein each of the M ultrasonicfrequencies differs from an adjacent ultrasonic frequency by at least afirst frequency spacing. An encoder receives the plurality of datasignals. Each of the plurality of data signals is encoded by arespective set of Q of the M ultrasonic frequencies. A minimum frequencyseparation between any pair of the Q ultrasonic frequencies of anyrespective set is greater than the first frequency spacing.

In a second embodiment of the present invention, a method oftransmitting an ultrasonic signal through a conducting media isdisclosed. The method includes selecting a set of M ultrasonicfrequencies, wherein each of the M frequencies differs from an adjacentfrequency by at least a first frequency spacing. The method furtherincludes estimating a channel characteristic of the conducting media andselecting a minimum frequency separation in response to the estimate. Adata signal is encoded with a set of Q of the M ultrasonic frequencies,wherein a minimum frequency separation between any pair of the Qfrequencies of the set of Q frequencies is greater than the firstfrequency spacing. The encoded ultrasonic data signal through theconducting media.

In a third embodiment of the present invention, an ultrasoniccommunication system is disclosed. The system includes an ultrasonictransmitter arranged to produce a set of M ultrasonic frequencies,wherein each of the M frequencies differs from an adjacent frequency byat least a first frequency spacing. An encoder circuit encodes a datasignal with a set of Q of the M ultrasonic frequencies, wherein aminimum frequency separation between any pair of the Q frequencies ofthe set of Q frequencies is greater than the first frequency spacing. Afirst ultrasonic transducer adapted for connection to a conductive mediais coupled to transmit the set of Q ultrasonic frequencies.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

FIG. 1 is a simplified diagram of an ultrasonic communication system ofthe prior art;

FIG. 2 is a multitoned frequency-shift keyed (MFSK) encoding system ofthe prior art;

FIG. 3 is a diagram comparing frequency-shift keyed (FSK) bits/symbol tomultitoned frequency-shift keyed (MFSK) bits/symbol as a function of Qof N available tones;

FIG. 4 is a diagram of an ultrasonic communication system of the presentinvention;

FIG. 5A is a diagram comparing a 32 kHz transmitted waveform with acorresponding waveform received through a 10 meter copper pipe;

FIG. 5B is a diagram comparing the frequency domain of a 40.25 kHztransmitted waveform with a corresponding frequency domain of thewaveform received through a 10 meter copper pipe;

FIG. 6A is a table showing symbol error rate (SER) and throughput as afunction of minimum tone separation (MTS);

FIG. 6B is a diagram showing symbol error rate (SER) as a function ofminimum tone separation (MTS) as in FIG. 6A for 14 meter transducerseparation;

FIG. 6C is a diagram showing a percentage decrease in data rate as afunction of minimum tone separation (MTS) as in FIG. 6A for 14 metertransducer separation;

FIG. 7 is a flow chart showing a method of transmitting multitonefrequency-shift keyed (MFSK) encoded data with minimum tone separation(MTS) according to the present invention;

FIG. 8A is a flow diagram showing multitone frequency-shift keyed (MFSK)encoding of data with minimum tone separation (MTS) according to thepresent invention;

FIG. 8B is a frequency diagram corresponding to the flow diagram of FIG.8A;

FIG. 9A is a flow chart showing construction of matrices V and N;

FIGS. 9B and 9C are respective diagrams of matrices V and N;

FIG. 10A is a flow chart showing encoding a message with matrices V andN;

FIG. 10B is a flow diagram showing encoding of a message according tothe flow chart of FIG. 10A;

FIG. 11A is a flow chart showing decoding a message with matrices V andN; and

FIG. 11B is a flow diagram showing decoding of a message according tothe flow chart of FIG. 11A.

DETAILED DESCRIPTION OF THE INVENTION

The preferred embodiments of the present invention provide significantadvantages in symbol error rate (SER) and resulting data throughput ofultrasonic transmission through various conducting media over methods ofthe prior art as will become evident from the following detaileddescription.

Referring to FIG. 4, there is a simplified diagram of an ultrasoniccommunication system of the present invention. The system includes atransmitter 400 and receiver 404 communicating through an ultrasoniccommunication channel 402. The ultrasonic communication channel may besolid, fluid or gas media and may be situated in an environment wherewired or wireless communication is difficult. For example, theultrasonic communication channel 402 may be a metal pipe that waspreviously installed in a commercial or residential complex, a buriedpipe or conduit for fluid or gas transmission, a metal frame or supportstructure, or other conducting media. Moreover, the media may be aplastic material such as polyvinyl chloride (PVC), polyethylene (PE), orother conducting media. The present inventors have determined that awide variety of conducting media may be characterized as a multipathfading channel for conducting ultrasonic signals.

Transmitter 400 includes a multitone frequency-shift keyed (MFSK) mapperand encoder as will be explained in detail. The transmitter receives amessage m, which is preferably a sequence of N-bit data words, where Nis a positive integer. The communication system employs a selected setof M available tones, where M is a positive integer. The M tones orfrequencies may be spaced apart in a linear manner by a minimumfrequency spacing Δf. A set of Q of the tones are selected subject tominimum tone separation (MTS) from the set of M tones to encode eachN-bit data word, where N is less than or equal to an integer part oflog₂

$\begin{pmatrix}M \\Q\end{pmatrix}{\quad.}$

The selected Q tones representing an N-bit data word are subsequentlytransmitted during a symbol time Ts having a duty cycle θ by a firstultrasonic transducer (not shown) attached to the conductive media. Datathroughput of the system, therefore, is 1/Ts symbols/second or log₂

$\begin{pmatrix}M \\Q\end{pmatrix}/T_{S}$

bits/second. Receiver 404 receives the Q tones by a second ultrasonictransducer (not shown) attached to the conductive media. Receiver 404includes a noncoherent MFSK detector and mapper/decoder circuit. Thereceiver uses a fast Fourier transform (FFT) based peak detector tunedto each of the M frequencies. Q of the M frequencies are detected in thereceived signal. They are mapped and decoded to produce the sequence ofN-bit data words and reconstruct decoded message {circumflex over (m)}.

Turning now to FIG. 5A, there is a diagram comparing a transmitted 32kHz sinusoidal waveform with a corresponding waveform received through a10 meter copper pipe. The transmitted signal has a peak-to-peak voltageof 10 V and is scaled for comparison with the 1.3 mV peak-to-peakvoltage of the received signal. The received signal illustrates severemultipath fading that may occur in complex ultrasonic structures. Themagnitude of the adjacent side lobes of the received signal are onlyslightly less than the primary received signal. When superimposed onother of the Q tones in an N-bit data word, this may lead to detectionproblems and an increased symbol error rate (SER) at the receiver.

FIG. 5B is a diagram comparing the frequency domain of a 40.25 kHztransmitted waveform with a corresponding frequency domain of thewaveform received through a 10 meter copper pipe. The diagramillustrates a first side lobe of the transmitted signal at 40.55 kHz is14 dB less than the magnitude of the transmitted signal at 40.25 kHz.However, the first side lobe of the received signal is only 6 dB lessthan the magnitude of the received signal at 40.25 kHz. This isprimarily because the multipath channel does not equally attenuate eachfrequency. The receiver, therefore, may confuse a real peak of one ofthe Q transmitted tones with a side lobe of another tone of the Qtransmitted tones. This results in a detection errors and an increasedSER.

The present inventors have determined that significant a reduction inSER is possible with only a small reduction in data throughput byimplementing a minimum tone spacing (MTS) within the set of Q selectedtones representing a data word. This is illustrated by the table of FIG.6A. The inventors applied the MFSK system of FIG. 4 to a 10 meter copperpipe having a 2.5 cm diameter. An alphabet size of M=120 available toneswas used with a set of Q=4 tones in each symbol. This provides theinteger part of log₂

$\begin{pmatrix}120 \\4\end{pmatrix}{\quad{= {22\mspace{14mu} {bits}\text{/}{{symbol}.}}}}$

The selected ultrasonic frequency set F was 31.75 kHz+(k*0.25) kHz,where k=1, 2, . . . 120. This provides an available frequency range ofset M from 32 kHz to 61.75 kHz in 0.25 kHz steps. Referring again toFIG. 6, the left column shows the MTS constraint from 0 kHz to 5 kHz in1 kHz steps. The first row with 0 kHz MTS indicates no additional toneseparation, and the Q tones of a symbol may be separated by the 0.25 kHzspace of frequency alphabet M. For this implementation withoutadditional MTS the data rate is 575 bits/second. The symbol error rate(SER) for a transmitter-to-receiver transducer space of 5 meters was0.555. The SER of the first row for transmitter-to-receiver transducerspaces of 10 meters and 14 meters was 0.607 and 0.554, respectively. TheSER, therefore, was relatively unchanged in the indicated range oftransducer space.

The second row illustrates results for an MTS constraint of 1 kHz. Here,the Q tones of a symbol must be separated by at least 1 kHz. For thisimplementation the data rate is slightly reduced to 563 bits/second. TheSER of the second row, however, is significantly less than in the firstrow. For transmitter-to-receiver transducer spaces of 5, 10, and 14meters, the SER was 0.239, 0.296, and 0.316, respectively. The SER,therefore, was relatively unchanged in the indicated range of transducerspace. However, the average SER of the second row was 0.284 compared toan average SER of 0.572 for the first row without MTS. The second rowSER was advantageously less than half the first row SER with only a 2%reduction in throughput.

The third row illustrates results for an MTS constraint of 2 kHz. Here,the Q tones of a symbol must be separated by at least 2 kHz. For thisimplementation the data rate is slightly reduced to 546 bits/second or5% less than the first row. The SER of the third row, however, issignificantly less than in the first or second rows. Fortransmitter-to-receiver transducer spaces of 5, 10, and 14 meters, theSER was 0.191, 0.260, and 0.256, respectively. The average SER of thethird row was 0.236 compared to an average SER of 0.572 for the firstrow without MTS. This is a 59% decrease in SER with respect to the firstrow with only a 5% reduction in throughput. The SER is seen to decreasein subsequent rows with increasing MTS. In the fifth row for an MTSconstraint of 5 kHz, the average SER is 0.76 for an 87% decrease inaverage SER. The throughput, however, is 480 bits/second for athroughput reduction of 17%.

FIG. 6B is a diagram showing symbol error rate (SER) for atransmit/receive transducer separation of 14 meters as a function ofminimum tone separation (MTS) as previously discussed with regard to thetable of FIG. 6A. Likewise, FIG. 6C is a diagram showing a percentagedecrease in data rate for a transmit/receive transducer separation of 14meters as a function of minimum tone separation (MTS). FIGS. 6B and 6Cgraphically illustrate significant advantages of the present inventionover MFSK systems of the prior art.

Referring now to FIG. 7, there is a flow chart showing a method oftransmitting multitone frequency-shift keyed (MFSK) encoded data signalswith minimum tone separation (MTS) according to the present invention.The method includes selecting M tones 700, where M is a positiveinteger. Each of the M tones is generated by an ultrasonic transmitteras in FIG. 4 and has a frequency separation of Δf. The method includesestimating a channel characteristic 702 of the conducting media throughwhich the MFSK encoded data signals will be transmitted. The channelestimate may be based on the type of conducting media, the length andwall thickness of the media, whether the media is conducting a fluid,whether the media is buried, or other factors that affect the channelcharacteristic. The channel characteristic may also be estimatedempirically by transmitting a known ultrasonic data signal through themedia and observing the received signal. Moreover, the known ultrasonicdata signal may include a range of frequencies to determine the effectof the multipath fading channel. At step 704, a minimum frequency(f_(min)) or tone separation (MTS) greater than Δf is selected tominimize side lobe interference as previously discussed. A data word isreceived at step 706 and encoded at step 708 with a respective set of Qof the M tones. Each of the Q tones in the respective set is separatedby at least the selected MTS of step 704. At step 710 the respective setof Q ultrasonic tones representing the encoded data word is transmittedthrough the conducting media to a remote receiver. Step 712 determinesif there is more data to be transmitted. If so, control returns to step706 to receive the next data word. If not, the method ends at step 714.

Referring next to FIG. 8A, there is a flow diagram showing multitonefrequency-shift keyed (MFSK) encoding of data with minimum toneseparation (MTS) according to the present invention. Here and in thefollowing discussion, tones and frequencies are used interchangeably. Ineach case, the following diagrams include indices that will be used toselect the tones or frequencies. The diagram begins at block 800 withselection of M tones of frequency set F₀ and the MTS f_(min) constraintas previously described with respect to blocks 700-704 of FIG. 7. Block802 selects Q of the M tones as described at block 708. The selectionprocess of block 802 begins at block 804 where a first of Q frequenciesf¹ is selected from set F₁ such that a difference between currentfrequency f and first frequency f¹ is greater than MTS constraintf_(min). Next at block 806, the second of Q frequencies f² is selectedfrom set F₂ such that a difference between current frequency f andsecond frequency f² is greater than MTS constraint f_(min). The processcontinues and at block 808 the frequency f^(Q-1) is selected from setF_(Q-1) such that a difference between current frequency f and frequencyf^(Q-1) is greater than MTS constraint f_(min). Finally, frequency f^(Q)is selected from F_(Q-1) such that a difference between frequencyf^(Q-1) and frequency f^(Q) is greater than MTS constraint f_(min). Eachof the Q selected frequencies f¹ through f^(Q) is applied to a selectedsine wave generator. The resulting Q sine waves are then summed atcircuit 812 to produce an MTS constrained MFSK signal.

FIG. 8B is a frequency diagram corresponding to the flow diagram of FIG.8A. There are M available tones or frequencies along the vertical axis.Each Q-tone codeword is selected from a unique combination of frequencysets F₀ 820, F₁ 822, F₂ 824, through F_(Q-1) 826. Each tone of a Q-tonecodeword is separated from other tones of the codeword by at leastf_(min) as indicated by the offset of each frequency set. Therefore,only L tones from each frequency set may be used, where L is defined byequation [1] and n_(min) is an integer difference of indicescorresponding to f_(min).

L=M−n _(min)×(Q−1)  [1]

Each frequency set includes an unused set of tones as indicated byshaded regions 830-834. For example, frequency set F₀ 820 includes Lused tones and (Q−1)×f_(min) unused tones 830. The unused tones of the Mavailable tones in each frequency set permit the f_(min) frequencyseparation in each Q-tone codeword. A total of T Q-length codewords,therefore, may be formed subject to an n_(min) MTS constraint as shownat equation [2] as will be explained with reference to FIGS. 9A and 9B.

$\begin{matrix}{T = {\sum\limits_{i = 1}^{L}n_{i,1}}} & \lbrack 2\rbrack\end{matrix}$

FIG. 9A is a flow chart showing construction of matrices V and N, asshown at respective FIGS. 9B and 9C. Each of matrices V and N have Lrows and Q columns corresponding to the L used frequencies of eachfrequency set and the Q tones of each codeword. Matrix V, havingelements v_(i,j), and matrix N, having elements n_(i,j), form a trellisfor encoding each message m, as will be discussed in detail. The flowchart begins at block 900 where M, Q, and n_(min) are input. At block902, L is calculated according to equation [1], and n_(i,Q) is set to 1for all i from 1 to L at block 904. Index j is initialized at block 906to Q at an outer loop structure that terminates at block 918 anddecrements j by 1 until it is equal to 1. Index i is initialized atblock 908 to 1 at an inner loop structure that terminates at block 916and increments i by 1 until it is equal to L. Block 910 computes matrixelements v_(i,j) for matrix V. Block 914 computes matrix elementsn_(i,j) for matrix N if index j is less than Q according to test 912.Completion of the nested loop structure produces matrices V and N atblock 920 as shown at respective FIGS. 9B and 9C.

Turning now to FIG. 10A, there is a flow chart showing encoding amessage m with matrices V and N from FIGS. 9A through 9D. In thefollowing examples, M=6 available tones, n_(min)=2, L=2 (equation [1]),matrices V and N are 2×3, and message m=3. The flow chart begins atblock 1000 where m, Q, and matrices V and N are input. Operation of theflow chart will now be explained with reference to the flow diagram ofFIG. 10B. The flow chart begins at block 1000 where message m, codewordlength Q, and matrices V and N are input. At block 1002, variable m₁ isset to message m, which is 3 for this example as shown at level 1 ofFIG. 10B. Index i_(j) is initially set to 1 for all j from 0 to Q=3. Atblock 1004, a loop begins with index j incremented from 1 to Q byincrement 1. On a first pass through the loop, test 1006 determineswhether m₁=3 is greater than a sum, which is only element n_(1,1)=3. Theresult is false (F), and control passes to block 1010. Here, the initialvalue of i=1 is greater than the final value of i=0, so the sum ofn_(i,j) is set to 0. Thus, m₂ is set to m₁ as shown at level 2 of FIG.10B. At block 1012, i₂ is set to i₁=1. At block 1014, the first elementof codeword c is set to c₁=v_(1,1)=1. Node 1016, terminates the firstpass through the loop, and control passes to block 1004 where j isincremented to 2.

On a second pass through the loop, test 1006 determines whether m₂=3 isgreater than a sum, which is only element n_(1,2)=2. The result is true(T), and control passes to block 1008. Index i₂ is incremented to 2 andcontrol passes to test 1006. Now test 1006 determines whether m₂=3 isgreater than a sum of n_(1,2)+n_(2,2)=3. The result is false (F), andcontrol passes to block 1010. Here, m₃ is set to m₂−2=1, as shown atlevel 3 of FIG. 10B. At block 1012, i₃ is set to i₂=2. At block 1014,the second element of codeword c is set to c₂=v_(2,2)=4. Node 1016,terminates the second pass through the loop, and control passes to block1004 where j is incremented to 3.

On a third pass through the loop, test 1006 determines whether m₃=1 isgreater than a sum, which is only element n_(2,3)=1. The result is false(F), and control passes through unused blocks 1010 and 1012 to block1014. Here, the final element of codeword c is set to c₃=v_(2,3)=6. Node1016, terminates the loop, and control passes to block 1018 wherecodeword c is output. Thus, the set Q {1,4,6} of M frequencies areencoded for transmission by the circuit of FIG. 8A through a conductivemedia via an ultrasonic transducer to a remote receiver.

Referring now to FIG. 11A, there is a flow chart showing backpropagation decoding by an ultrasonic receiver of the codeword c thatwas encoded as discussed with regard to FIGS. 10A and 10B. Operation ofthe flow chart will now be explained with reference to the flow diagramof FIG. 11B. The flow chart begins at block 1100 where c, L, Q, andmatrices V and N are input. Codeword c is received by the ultrasonicreceiver via an ultrasonic transducer attached to the conductive media.Matrices V and N are calculated by the receiver in the same manner aspreviously described with reference to FIGS. 9A and 9B. Indices i₁through i₃ are initially set to 1, 2, and 2, respectively. At block1104, index i₀ is set to 1. At block 1106, m₃ is set to n_(2,3)=1 asshown at level 3 of FIG. 11B. At block 1108, a loop begins with index jinitially set to Q−1=2 and decreasing to 1 by decrement −1. On a firstpass through the loop, block 1110 sets m₂ to m₃+n_(1,2)+n_(2,2)=3, asshown at level 2 of FIG. 11B. Node 1112, terminates the first passthrough the loop, and control passes to block 1108 where j isincremented to 1. On the second and final pass through the loop, block1110 sets m₁ to m₂+n_(1,1)=3, as shown at level 1 of FIG. 11B. Node1112, terminates the final pass and control passes to block 1114, wheremessage m is set to m₁=3. Original message m=3 is output to completedecoding.

The foregoing embodiments of the present invention advantageouslyprovide multitone frequency-shift keyed (MFSK) communication withminimum tone separation (MTS). Another embodiment of the presentinvention describes an efficient trellis-based encoding algorithm usingforward propagation. Yet another embodiment of the present inventiondescribes an efficient trellis-based backward propagation decodingalgorithm. Embodiments of the present invention greatly improve SER forall transmit/receive transducer separation distances. Side lobeinterference of adjacent tones subject to the MTS constraint are greatlyreduced. Data throughput may be slightly reduced or may even be improvedwith the improved SER. Encoding and decoding algorithms provideefficient communication with minimal computational complexity.

Still further, while numerous examples have thus been provided, oneskilled in the art should recognize that various modifications,substitutions, or alterations may be made to the described embodimentswhile still falling within the inventive scope as defined by thefollowing claims. Other combinations will be readily apparent to one ofordinary skill in the art having access to the instant specification.

1. A method of encoding a plurality of data signals, comprising:selecting a set of M ultrasonic frequencies, wherein each of the Mfrequencies differs from an adjacent frequency by at least a firstfrequency spacing, and wherein M is a positive integer; receiving theplurality of data signals; and encoding each of the plurality of datasignals by a respective set of Q of the M ultrasonic frequencies,wherein Q is a positive integer less than M, and wherein a minimumfrequency separation between any pair of the Q frequencies of anyrespective set is greater than the first frequency spacing.
 2. Themethod of claim 1, comprising: estimating a characteristic of a channelfor transmitting each respective set of the Q ultrasonic frequencies;and selecting the minimum frequency separation in response to the stepof estimating.
 3. The method of claim 1, comprising transmitting eachset of the Q ultrasonic signals through a conducting media at arespective time.
 4. The method of claim 1, comprising transmitting eachrespective set of the Q ultrasonic signals through a conducting media toa remote receiver.
 5. The method of claim 4, wherein the conductingmedia is a metal pipe.
 6. The method of claim 4, wherein the conductingmedia is a plastic pipe.
 7. The method of claim 1, wherein each datasignal is an N-bit data word, wherein N is a positive integer, andwherein N is less than an integer part of log₂ $\begin{pmatrix}M \\Q\end{pmatrix}{\quad.}$
 8. The method of claim 1, wherein the minimumseparation between any pair of the Q frequencies is n_(min) of the Mfrequencies.
 9. The method of claim 8, wherein each of the Q frequenciesis selected from a respective set of L of the M frequencies, whereinL=M−n_(min)(Q−1).
 10. A method of transmitting an ultrasonic signalthrough a conducting media, comprising: selecting a set of M ultrasonicfrequencies, wherein each of the M frequencies differs from an adjacentfrequency by at least a first frequency spacing, and wherein M is apositive integer; estimating a channel characteristic of the conductingmedia; selecting a minimum frequency separation in response to the stepof estimating; receiving a data signal; encoding the data signal with aset of Q of the M ultrasonic frequencies, wherein Q is a positiveinteger less than M, and wherein a minimum frequency separation betweenany pair of the Q frequencies of the set of Q frequencies is greaterthan the first frequency spacing; and transmitting the encodedultrasonic data signal through the conducting media.
 11. The method ofclaim 10, comprising transmitting each set of the Q ultrasonic signalsthrough a conducting media at a respective time.
 12. The method of claim10, comprising transmitting each respective set of the Q ultrasonicsignals through a conducting media to a remote receiver.
 13. The methodof claim 12, wherein the conducting media is a metal pipe.
 14. Themethod of claim 10, wherein each data signal is an N-bit data word,wherein N is a positive integer, and wherein N is less than an integerpart of log₂ $\begin{pmatrix}M \\Q\end{pmatrix}{\quad.}$
 15. An ultrasonic communication system,comprising: an ultrasonic transmitter arranged to produce a set of Multrasonic frequencies, wherein each of the M frequencies differs froman adjacent frequency by at least a first frequency spacing, and whereinM is a positive integer; an encoder circuit arranged to encode a datasignal with a set of Q of the M ultrasonic frequencies, wherein Q is apositive integer less than M, and wherein a minimum frequency separationbetween any pair of the Q frequencies of the set of Q frequencies isgreater than the first frequency spacing; and a first ultrasonictransducer adapted for connection to a conductive media and coupled totransmit the set of Q ultrasonic frequencies.
 16. The system of claim15, comprising: a second ultrasonic transducer adapted for connection tothe conductive media and coupled to receive the set of Q ultrasonicfrequencies. an ultrasonic receiver arranged to receive the set of Qultrasonic frequencies from the second ultrasonic transducer; a detectorcircuit arranged to detect the set of Q ultrasonic frequencies; and adecoder circuit arranged to decode the Q ultrasonic frequencies andproduce the data signal.
 17. The system of claim 15, wherein the minimumfrequency separation is selected in response to a channel estimate ofthe conductive media.
 18. The system of claim 17, wherein the channelestimate is a function of a length of the conductive media.
 19. Thesystem of claim 17, wherein the channel estimate is a function of a wallthickness of the conductive media.
 20. The system of claim 15, whereinthe data signal is an N-bit data word, wherein N is a positive integer,and wherein N is less than an integer part of log₂ $\begin{pmatrix}M \\Q\end{pmatrix}{\quad.}$